An improvement to double-step Newton method and its multi-step version for solving system of nonlinear equations and its applications

被引：14
|
作者：
Madhu, Kalyanasundaram [1 ]
Babajee, D. K. R. [2 ]
Jayaraman, Jayakumar [1 ]
机构：
[1] Pondicherry Engn Coll, Dept Math, Pondicherry 605014, India
[2] 65 Captain Pontre St, St Croix 11708, Port Louis, Mauritius
来源：
NUMERICAL ALGORITHMS | 2017年 / 74卷 / 02期
关键词：
System of nonlinear equation; Newton's method; Order of convergence; Multi-step method; Frechet derivatives;
D O I：
10.1007/s11075-016-0163-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this work, we have improved the order of the double-step Newton method from four to five using the same number of evaluation of two functions and two first order Fr,chet derivatives for each iteration. The multi-step version requires one more function evaluation for each step. The multi-step version converges with order 3r+5, r >= 1. Numerical experiments are done comparing the new methods with some existing methods. Our methods are also tested on Chandrasekhar's problem and the 2-D Bratu problem to illustrate the applications.
引用
收藏
页码：593 / 607
页数：15
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